It's about four in the afternoon, and hot as you know May can be: as hot as any summer day, but lighter somehow. It's perfect, in other words. There's no need to hurry, either. My second afternoon in Normandy I have learnt that. In planning this fishy escape I emailed Adrian and Hedy, English owners of the French manoir at my back, wondering whether Gallic mayfly were any different from English ones, if they hung about on the left bank only, smoking Gauloises, reading Sartre.

Now I know at least that they get up later. Just a few are already riding the current of the river I'm facing, like miniature, yellow-sailed yachts.

Except once in a while, when one of these yachts sinks into a whorl of water just under the trailing branch of alder off the far bank. The water is darker there and deeper. Just the right place for a fat trout. In a minute I'll sneak through the rushes and catch it. But as I said, it's France: there's no need to hurry.

The mayfly is an upwinged river-fly you might have half-noticed yourself if you have ever taken a riverside walk in the south country around mid-May. It will have been flitting over the stream, catching the light: a diaphanous finale to a rather muddy existence. Two years wriggling through silt on the river bed. One day afloat on gossamer wings.

It's hard to believe the fuss it causes, that this insect is the fervid epicentre of a fortnight-long carnival, a sort of fisherman's Glastonbury. The mayfly is so big, and it hatches in such abundance, that trout go crazy for it and lose all caution.

And so mayfly fortnight is popularly called "duffers' fortnight": a time when any old fool can trick a trout with a fake mayfly and a hook. And so cabin-fevered anglers bolt south and west from London to the banks of the Test or the Kennet, coughing up hundreds of pounds a day for the privilege of casting into those hallowed waters to catch a whopper.

The festivities are distinctly Home Counties. It's within a two-hour drive of London – more job-shackled anglers, more money, more mayflies, fatter trout – that the frenzy is most intense. It's the chalk-stream setting that puts the proscenium arch around the whole aquatic opera. Clear streams flowing through rolling chalk hills. Cool, spring water just right for growing fat flies and fish.

Traditionally, then, it's all very three-o'clock-from-Waterloo, very thatched cottage, very real ale, very English. A fabulous tonic for a bad case of the office-nasties. But lacking also a certain… exoticism, a certain je ne sais quoi. Put it this way, those Waterloo-to-Winchester, or M3-southbound, anglers are most often alone. They are sans femme, sans famille.

It doesn't have to be like that. The chalk hills that create those cream-tea rivers of ours don't stop at Portsmouth. They dip under the Channel and resurface around Caen, before they are lost again to the layering of the Earth. And in that brief interlude they bubble up a handful of chalk streams with a French accent: the Risle, the Charentonne and the Andelle.

These are names that play in French angling legend, rivers that Eisenhower, Hemingway and Ritz fished. And of course they flow through French countryside, French villages, past cafés and restaurants and, in the case of the one where I'm sitting right now, the grounds of a private manoir where you can stay on the top floor with views to the silent woods all around, and be absurdly well fed, wined and watered.

Now that this afternoon's hatch has begun it will only get busier – a warm day is best, perhaps with more cloud than this one, though I'm not complaining – until six the air will be full of flickering specks and the river's surface will be broken everywhere I look with the widening rings of rising trout. I'll fish until the gloaming, catch a hatful and stroll from the river back across the lawn to the manoir for supper.

This walled manoir, almost chateau, has already become the place I would most like-to live in the whole world. It has a Xanadu quality to it: the wall does not quite enfold the entire 80 acres of wetland, stream and meadow, but it does shelter the house and an acre of lawn and rampant rosemary.

Just outside the fortified walls there are vegetable beds and beehives. Beyond, in more or less every nook of woodland, are springs bubbling up clear water that seeps into the Andelle river.

The river itself is perfection: it meanders, it has slow, deep bends, fast riffles. It splits around an island – on which we ate supper last night, lamb roasted over an open fire, eaten under a chandelier suspended from a tree – and here and there are the stone remnants of the time when the river was the heart of a system of watermeadows.

It is hard to believe that this Sleeping Beauty stream was once lost behind a curtain of brambles, undergrowth and overgrowth, that Adrian and Hedy had to slash their way through to find it.

They had bought the house after many years of searching and moved here from the Isle of Man without any experience of trout streams or trout fishing. The river was mentioned in the sales particulars, but without emphasis.

It was, they discovered, the rivery equivalent of finding a Monet in the sitting room, hidden behind the curtain and inches of grime and dust. All this otherwise delightful stream needed was a little daylight to kick off the ecosystem: algae, bugs, weeds, trout, birds and bees.

And now they have done it, boy has it worked. This fish opposite me must have bellyache by now, and a few more have joined in, upstream and down. The sticky, still evening and its rural French quiet, punctuated by the plip and plop of trout having a party. I pick up my fishing rod and slither through a stand of yellow flag-iris and rushes at the water's edge.

I have on the line a mayfly pattern tied in homage to the "Andelle" fly. As accurately as I can, I try to place it so that it will float downstream into the sight of this trout. But the best trout lie in tricky places.

Finally I get it just right, the web of feathers and deceit bobs on the riffle and – gloop! – disappears into the same deadly whirlpool that has engulfed two dozen real flies already this afternoon.

The Manoir de Malvoisine is a listed fortified manoir dating from the 12th century. Over eight centuries it played its part in the Hundred Years war, the French Wars of Religion and even the Allied landings at Normandy. Now it is Adrian and Hedy Thompson's home, the top floor of which includes four double bedrooms for guests.

If you stay there you have the river and grounds to yourself. Rooms cost from €160 (£137) per night (breakfast €15/£13). Fishing on the Andelle costs €80 (£69) per rod per day from April to September.

Other places to go fly fishing in France

Le Pont de L'Hospital

In the heart of Corrèze on the banks of the River Maronne, this is a charming hotel run by James and Fiona Mallows. Fish on the rivers Maronne, Cere, Doustre, Souvigné or the Dordogne itself. Make sure you book a day with Jean-Pierre Coudoux, a guide who will teach you ways of fishing you didn't know were possible. In Argentat, at the boutique fly shop Mouche Guy Plas, you can buy flies tied with feathers from a special Correzian chicken, flies that glint in a way that trout find impossible to resist.

Another spring-fed French stream is La Sorgue, in Provence, where the fishing is a real challenge. It's here that the French national fly-fishing team practises – and it is consistently the best team in the world. The river is clear and beautiful and full of fish. You can canoe on it, too, from Fontaine all the way to l'Isle sur la Sorgue. Or go swimming at Partage des Eaux.

The local fly shop is called Le Sorguett: you can buy a permit there and arrange guides. Keep an eye out, too, for the special fly-fishing vest named after the river. For accommodation try: Domaine de la Fontaine, an old farmhouse on the outskirts of l'Isle sur la Sorgue (www.domainedelafontaine.com) or La Masion sur la Sorgue, a 17th-century hotel in the historic centre of l'Isle sur la Sorgue a few steps from the basilica and the River Sorgue.

La Loue is a spring-fed river in Franche Compté near the Swiss border. It is one of the best trout and grayling rivers in France and one of the few where there are sections that are catch-and-release only.